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KCET2019MathematicsMatrices

If ( 3 A+4 B^ = [ array ccc 7 & -10 & 17 0 & 6 & 31 array ] ) and ( 2 B-3 A^ = [ array cc -1 & 18 4 & 0 5 & -7 array ] ) then ( B= )

Options

  1. A( [ array cc 1 & -3 -1 & 1 2 & 4 array ] )
  2. B( [ array cc 1 & 3 -1 & 1 2 & -4 array ] )
  3. C( [ array cc 1 & 3 -1 & 1 2 & 4 array ] )
  4. D( [ array cc -1 & -18 4 & -16 -5 & -7 array ] )

Correct answer

C. ( [ array cc 1 & 3 -1 & 1 2 & 4 array ] )

Step-by-step solution

(C) ( 3 A+4 B^ = [ array ccc 7 & -10 & 17 0 & 6 & 31 array ] .(1) ) ( (2 B-3 A^ )^ =(2 B)^ - (3 A^ )^ =2 B^ -3 A ) ( 2 B^ -3 A= [ array ccc -1 & 4 & -5 18 & 0 & -7 array ] .(2) ) (1) (2) Adding (1) and (2) we get, ( 6 ~B ^ = [ array ccc 6 & -6 & 12 18 & 6 & 24 array ] ) [ array l B^ = [ array ccc 1 & -1 & 2 3 & 1 & 4 array ] B= [ array ccc 1 & 3 & -1 & 1 & 2 & 4 & array ] array ]

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